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{ COMPLEX+TIME.PDE

 

 This example shows the use of complex variables in time-dependent systems.

 

 The equation that is solved is not intended to represent any real application.

 

}  

 

title 'Complex transient equations'  

 

Variables  

   U(0.01) = complex (Ur,Ui)         { creates variables Ur and Ui  }  

 

definitions  

   u0 = 1-x^2-y^2  

   s = complex(4,x)  

 

equations  

  { create two scalar equations, one for Ur and one for Ui }  

   U:  del2(U) +s = dt(U)  

 

boundaries  

  Region 1  

      start(-1,-1)  

      natural(Ur)=u0-Ur  

        line to (1,-1) to (1,1) to (-1,1) to close  

 

time 0 to 1  

 

plots  

for cycle=10  

      contour(Ur,Ui)  

      contour(Real(u),Imag(U))  

      contour(U)  

      vector(U)  

      elevation(u,s) from(-1,0) to (1,0)  

      history(u,s) at (0,0)  

 

end